Question

I have a ring with uniform charge Q. Calculate the electric field at any point around the x-axis. I arrived to a really hard integral that I will put in the comments. Any easier solution?

Answer 1

\[E _{p}=k _{e}\lambda R (x _{p}\int\limits\limits_{0}^{2\pi}\frac{ d \theta }{ (x _{p}^{2}-2Rx _{p} \cos \theta +R ^{2})^{3/2}}-R \int\limits\limits_{0}^{2\pi}\frac{ \cos \theta d \theta }{ (x _{p}^{2}-2Rx _{p}\cos \theta +R ^{2})^{3/2} })\]Where ke:electric constant; lambda: linear charge density.